Cfrgtkky

I am trying to follow the computation of EKF presented in this paper http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=C9CB210A45F0D7ED5CA7DE174F1A5490?doi=10.1.1.681.8390&rep=rep1&type=pdf (p.16-18), with the only difference that my system state does not include the acceleration, so it is a $4x1$ matrix:

$$x_x(t) = begin{bmatrix}
x(t) \
v_x(t) \
y(t) \
v_y(t)
end{bmatrix} $$
where $x(t)$ and $y(t)$ are the cartesian coordinates and $v_x(t)$ and $v_y(t)$ are the velocity components.

I have problem computing the State Estimate Update step (eq. 17 in the paper), where the measurement residual needs to be calculated. According to the paper, the State Estimate Update is:

$$hat{x}_x(k^{+}) = hat{x}_x(k^{-}) + K(k)[z_{z}(k)-h(hat{x}_x(k^{-}))]$$

where
$$z_z(k) = begin{bmatrix}
z_x(k) \
z_y(k)
end{bmatrix},
$$
where $z_x(k)$ and $z_y(k)$ are the measurements of $x$ and $y$ positions and
$$
h(x_x(k)) = begin{bmatrix}
x(k) &0 &0 &0 \
0 &0 &y(k) &0
end{bmatrix}. $$

$K(k)$ is the Kalman Gain, which in my case is a $4x2$ matrix.

My question is, how do I subtract $h(hat{x}_x(k^{-}))$ which is a $2x4$ matrix from $z_z(k)$, which is a $2x1$ matrix?
If I am not mistaken, the result of $K(k)[z_{z}(k)-h(hat{x}_x(k^{-}))]$ needs to be a $4x1$ matrix so that I can later add it to the previous estimate $hat{x}_x(k^{-})$, which is also $4x1$.

I suspect it is a mistake and the actual equation should have been

$$
h(x(k)) = begin{bmatrix}
1 & 0 & 0 & 0 & 0 & 0 \
0 & 0 & 1 & 0 & 0 & 0
end{bmatrix} x(k).
$$

In this case equation $(9)$ would also make more sense. So in your case it would be

$$
h(x(k)) = begin{bmatrix}
1 & 0 & 0 & 0 \
0 & 0 & 1 & 0
end{bmatrix} x(k).
$$